MEMCoder: Multi-dimensional Evolving Memory for Private-Library-Oriented Code Generation

Large Language Models (LLMs) excel at general code generation, but their performance drops sharply in enterprise settings that rely on internal private libraries absent from public pre-training corpora. While Retrieval-Augmented Generation (RAG) offers a training-free alternative by providing static API documentation, we find that such documentation typically provides only isolated definitions, leaving a fundamental knowledge gap. Specifically, LLMs struggle with a task-level lack of coordination patterns between APIs and an API-level misunderstanding of parameter constraints and boundary conditions. To address this, we propose MEMCoder, a novel framework that enables LLMs to autonomously accumulate and evolve Usage Guidelines across these two dimensions. MEMCoder introduces a Multi-dimensional Evolving Memory that captures distilled lessons from the model's own problem-solving trajectories. During inference, MEMCoder employs a dual-source retrieval mechanism to inject both static documentation and relevant historical guidelines into the context. The framework operates in an automated closed loop by using objective execution feedback to reflect on successes and failures, resolve knowledge conflicts, and dynamically update memory. Extensive evaluations on the NdonnxEval and NumbaEval benchmarks demonstrate that MEMCoder substantially enhances existing RAG systems, yielding an average absolute pass@1 gain of 16.31%. Furthermore, MEMCoder exhibits vastly superior domain-specific adaptation compared to existing memory-based continual learning methods.

Think Anywhere in Code Generation

Recent advances in reasoning Large Language Models (LLMs) have primarily relied on upfront thinking, where reasoning occurs before final answer. However, this approach suffers from critical limitations in code generation, where upfront thinking is often insufficient as problems' full complexity only reveals itself during code implementation. Moreover, it cannot adaptively allocate reasoning effort throughout the code generation process where difficulty varies significantly. In this paper, we propose Think-Anywhere, a novel reasoning mechanism that enables LLMs to invoke thinking on-demand at any token position during code generation. We achieve Think-Anywhere by first teaching LLMs to imitate the reasoning patterns through cold-start training, then leveraging outcome-based RL rewards to drive the model's autonomous exploration of when and where to invoke reasoning. Extensive experiments on four mainstream code generation benchmarks (i.e., LeetCode, LiveCodeBench, HumanEval, and MBPP) show that Think-Anywhere achieves state-of-the-art performance over both existing reasoning methods and recent post-training approaches, while demonstrating consistent generalization across diverse LLMs. Our analysis further reveals that Think-Anywhere enables the model to adaptively invoke reasoning at high-entropy positions, providing enhanced interpretability.

Do Transformers Have the Ability for Periodicity Generalization?

Large language models (LLMs) based on the Transformer have demonstrated strong performance across diverse tasks. However, current models still exhibit substantial limitations in out-of-distribution (OOD) generalization compared with humans. We investigate this gap through periodicity, one of the basic OOD scenarios. Periodicity captures invariance amid variation. Periodicity generalization represents a model's ability to extract periodic patterns from training data and generalize to OOD scenarios. We introduce a unified interpretation of periodicity from the perspective of abstract algebra and reasoning, including both single and composite periodicity, to explain why Transformers struggle to generalize periodicity. Then we construct Coper about composite periodicity, a controllable generative benchmark with two OOD settings, Hollow and Extrapolation. Experiments reveal that periodicity generalization in Transformers is limited, where models can memorize periodic data during training, but cannot generalize to unseen composite periodicity. We release the source code to support future research.

EvoCoT: Overcoming the Exploration Bottleneck in Reinforcement Learning

Reinforcement learning with verifiable reward (RLVR) has become a promising paradigm for post-training large language models (LLMs) to improve their reasoning capability. However, when the rollout accuracy is low on hard problems, the reward becomes sparse, limiting learning efficiency and causing exploration bottlenecks. Existing approaches either rely on stronger LLMs for distillation or filter out difficult problems, which limits scalability or restricts reasoning improvement through exploration. We propose EvoCoT, a self-evolving curriculum learning framework based on two-stage chain-of-thought (CoT) reasoning optimization. EvoCoT constrains the exploration space by self-generating and verifying CoT trajectories, then gradually shortens them to expand the space in a controlled way. This enables LLMs to stably learn from initially unsolved hard problems under sparse rewards. We apply EvoCoT to multiple LLM families, including Qwen, DeepSeek, and Llama. Experiments show that EvoCoT enables LLMs to solve previously unsolved problems, improves reasoning capability without external CoT supervision, and is compatible with various RL fine-tuning methods. We release the source code to support future research.